LEWIS. — FREE ENERGY AND EQUILIBRIUM. 9 



normal to the surface, and in "which the effects of gravity, surface tension, 

 etc. may be neglected. 



A necessary and sufficient condition for equilibrium is, that any change 

 in a system in equilibrium is reversible. In other words, the change in 

 the free energy of the system must be equal to the external work.* 



In the case under consideration the external work is the product of the 

 external pressure, P, by the change, F, in the volume of the system. 

 Therefore in equilibrium, 



A = PV. (11) 



Let us consider a system, of any degree of complexity, which is capa- 

 ble of change. In general this change will consist in a loss by some 

 constituents of the system, accompanied by a corresponding gain by 

 others. Then according to equation (G), 



r "-r' fTp — C 



A = RT\n L /-'„/•••- T " ... >->dT+HT+ U, 



''l '<" 1 * • • • J T I 



where quantities with subscript 1 refer to the constituents which suffer 

 loss; those with subscript 2, to those which gain, and n v n\, etc., and 

 a.,, ji'n, etc. represent the number of gram-molecules of each constitu- 

 ent lost and gained respectively. 



Combining equations (G) and (11) we have as the general equation of 

 equilibrium, 



PV=HTln 7„, '" -W ' *dT+BT+U, (11 o) 



J>1 » V i l . . . J 1 



where P is the external pressure and J 'is the total change in volume. 

 I ' i //, r, + n' 2 v' 2 +...)- (/?! v x -f n\ r\ +...). 



This equation (11 a) expresses the equilibrium of the system in regard 

 to the particular change in question. When a system is in perfect equi- 

 librium there will be an equation of the above form for every change or 

 reaction which can take place independently. These equations, however, 

 will not all be independent. For example, if both liquid and gaseous 

 acetic acid are composed of two kinds of molecules, namely. CH 3 COOII 

 and (CH g COOH) 2 , then when acetic acid and its vapor are in equilib- 



* Of course the change must not be great enough to disturb the condition of 

 equilibrium. The following demonstration would be somewhat more rigorous if 

 the infinitesimal notation were used. 



